What is the intended workflow to fix this UV issue?
As per Gilderman's comment, the problem is that I was using U>Unwrap. Simply using U>Smart UV Project fixed both of the issues I mention above, producing this much more reasonable UV mapping:



Observe how the concave planar ngon is correctly mapped isometrically (that is, both conformally and authalically) into UV space, and the same is true of the big square floor ngon. In fact, every single face ended up being mapped isometrically; exactly what I wanted.